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本文将二值逻辑代数推广为多值逻辑代数,并提出了一种新的基于多值逻辑代数理论的多状态系统的分析方法。二状态情况下的串联和并联结构函数被推广到多状态情况;二状态分析中使用的故障树被推广为状态树。使用本文中所定义的多值逻辑代数能够很方便的处理其基本结构形式为串联和并联的多状态系统。作为本文提出的多值逻辑代数和分析方法的应用,文中最后简略分析了两种多状态系统;(1)由具有两类失效模式的元件组成的多状态系统;(2)考虑元件的性能水平和系统的性能水平的一种多状态系统。给出了计算这两种多状系统取某一状态概率的计算方法。
This paper extends binary logic algebra to multi-valued logic algebra, and proposes a new multi-state system analysis method based on multi-valued logic algebra theory. The tandem and parallel structural functions in the second state are generalized to multi-state cases. The fault trees used in the second state analysis are generalized as state trees. The multi-valued logic algebra defined in this paper can be used to handle multi-state systems whose basic structure is in series and parallel. As an application of the multi-valued logic algebra and analysis method proposed in this paper, two kinds of multi-state systems are briefly analyzed in the end; (1) Multi-state systems composed of two types of failure modes; (2) And system performance level of a multi-state system. The calculation method of calculating the probability of a certain state of these two kinds of multi-state systems is given.